direction handles

I  am sure I completely understand you when you say "when two paths are connected at the same point."  If you mean that you have two bezier paths on the same layer and you have positioned the end vertex (point) of one path directly over the other path, then select the path in the timeline you want to edit, then select the Pen tool (g), then hover over one of the paths until the pen tool gets a little + sign to add a point, then hold down the Ctrl/Cmnd key to change the pen tool to the path selection tool (which looks a little like a ∆) and click on the path between two points. That specific path is now selected. You should then be able to hover any other point on the path and see the point selection tool. Clicking on one of the endpoints with the selection tool will reveal any bezier handles on that point. You can move them easily by holding down the Alt/Option key to change to the Convert Vertex tool (looks a little like a partially inverted V) to create or edit either path or just stay with the selection tool to grab the end of one of the handles. 

It's all about using the right selection tool. Generally the pen tool with modifier keys is the best option for getting a specific path selected, but sometimes, if you are animating a path, the selection tool works best if the path is already selected.